We present a study of the [C ii] 158 mu m line and underlying far-infrared (FIR) continuum emission of 27 quasar host galaxies at z similar to 6, traced by the Atacama Large Millimeter/submillimeter Array at a spatial resolution of similar to 1 physical kpc. The [C ii] emission in the bright, central regions of the quasars have sizes of 1.0-4.8 kpc. The dust continuum emission is typically more compact than [C ii]. We find that 13/27 quasars (approximately one-half) have companion galaxies in the field, at projected separations of 3-90 kpc. The position of dust emission and the Gaia-corrected positions of the central accreting black holes are cospatial (typical offsets less than or similar to 0.'' 1). This suggests that the central black holes are located at the bottom of the gravitational wells of the dark matter halos in which the z > 6 quasar hosts reside. Some outliers with offsets of similar to 500 pc can be linked to disturbed morphologies, most likely due to ongoing or recent mergers. We find no correlation between the central brightness of the FIR emission and the bolometric luminosity of the accreting black hole. The FIR-derived star formation rate densities (SFRDs) in the host galaxies peak at the galaxies' centers, at typical values between 100 and 1000 M-circle dot yr(-1) kpc(-2). These values are below the Eddington limit for star formation, but similar to those found in local ultraluminous infrared galaxies. The SFRDs drop toward larger radii by an order of magnitude. Likewise, the [C ii]/FIR luminosity ratios of the quasar hosts are lowest in their centers (few x10(-4)) and increase by a factor of a few toward the galaxies' outskirts, consistent with resolved studies of lower-redshift sources.